The problem here is you really haven't defined your photographic interests. Best is a variable dependent on your needs and expectations.

Besides defining yours needs I'm interested in how you came up with the original list of ~8 cameras and then reduced it to three. What was your criteria for either list?

The Fuji F20 lists at $300 US and using that as an upper limit there are literally dozens of very good cameras available but there characteristics are not identical. Some excel at some things while being good at others and other cameras excel at different things.

I'd suggest starting with Steve's Best Cameras list http://www.steves-digicams.com/best_cameras.html. Of the three cameras you've listed only the Fuji F20 shows up but neither Steve nor any other reviewer has tested all the cameras on your list so the fact that the others don't show up may only indicate they haven't been tested.

That said I have an issue with the F20 because it doesn't have an optical viewfinder which is a must in my PERSONAL criteria. Your mileage may vary.